期权期货及其衍生品第22弹.ppt

* * * * * * * * * * Results for SP 500 When instantaneous volatility changes by 1% Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Option Life (days) 10 30 50 100 500 Volatility increase (%) 0.97 0.92 0.87 0.77 0.33 Correlations and Covariances (515) Define xi=(Xi?Xi-1)/Xi-1 and yi=(Yi?Yi-1)/Yi-1 Also sx,n: daily vol of X calculated on day n?1 sy,n: daily vol of Y calculated on day n?1 covn: covariance calculated on day n?1 The correlation is covn/(sx,n sy,n) Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Updating Correlations We can use similar models to those for volatilities Under EWMA covn = l covn-1+(1-l)xn-1yn-1 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Positive Finite Definite Condition A variance-covariance matrix, W, is internally consistent if the positive semi-definite condition for all vectors w Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Example The variance-covariance matrix is not internally consistent Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Volatilities and Correlations for Four-Index on Sept 25, 2008 with Equal Weights DJIA FTSE CAC 40 Nikkei 225 DJIA 1 FTSE 0.489 1 CAC 40 0.496 0.918 1 Nikkei 225 ?0.062 0.201 0.211 1 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * DJIA FTSE CAC 40 Nikkei 225 Vol. per day (%) 1.11 1.42 1.40 1.38 Volatilities and Correlations for Four-Index on Sept 25, 2008 for EWMA and l=0.94 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * DJIA FTSE CAC 40 Nikkei 225 DJIA 1 FTSE 0.611 1 CAC 40 0.629 0.971 1 Nikkei 225 ?0.113 0.409 0.342 1 DJIA FTSE CAC 40 Nikkei 225 Vol. per day (%) 2.19 3.21 3.09 1.59 One-Day 99% VaR Estimates Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Histori